Contact-impact Problems with Shell and Beam Structures

Abstract

Abstract In engineering, shell and beam structures are very common and of great importance. In passenger cars and aircraft, for example, the majority of structures can be classified as shells or beams. Shell and beam structures can of course be modelled using the continuum elements described in the preceding chapters. However, they can be modelled more accurately and efficiently using shell and beam elements. A shell element is often represented by a reference surface with a number of nodes on it but still represents the behaviour of the material within a three-dimensional volume. Similarly, a beam element is represented by a reference line with a number of nodes on it but still represents the behaviour of the material within a three-dimensional volume. Great effort has been put into both theoretical and experimental studies of shells and beams. An abundant literature on shell and beam theories is now available, and so are a large number of useful shell and beam elements; see for example, Ahmad et al. (1970), Hughes and Liu (1981), Onate and Zienkiewicz (1983), Owen and Figueiras (1983), Belytschko et al. (1984a), Bergan and Nygard (1985), Owen et al. (1985), Park et al. (1985a,b), Stanley and Felippa (1985), Belytschko and Bachrach (1986), Ginsberg et al. (1986), Hallquit and Benson (1986), Onate and Oliver (1986), Parisch (1986), Park and Stanley (1986), Stanley et al. (1986), Belytschko and Engelman (1988), Chaudhuri (1988), and Noor et al. (1989). In this chapter, contact-impact problems involving shell and beam structures are studied.